Satellite image classification across multiple  resolutions and time using ordering constraint among instances

ABSTRACT

A method includes classifying low-resolution pixels of a low-resolution satellite image of a geographic area to form an initial classification map and selecting at least one physically-consistent classification map of the low-resolution pixels based on the initial classification map. A water level associated with at least one of the physically-consistent classification maps is then used to identify a set of high-resolution pixels representing a perimeter of water in the geographic area.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is based on and claims the benefit of U.S.provisional patent application Ser. No. 62/545,777, filed Aug. 15, 2017,the content of which is hereby incorporated by reference in itsentirety.

BACKGROUND

Remote sensing satellites capture images of different geographic areas.The resolution of such images and the time periods between whensuccessive images of the same geographic area are captured vary fromsatellite to satellite. After an image is captured, the contents of theimage must be analyzed to determine what is contained in the image. Insome systems, classifiers are used to classify each pixel as containinga particular type of land cover such as water or land. Together, thesepixel classifications provide a classification map that describes theland cover classification of each geographic sub-area within ageographic area. Because of the large number of images and the largenumber of pixels in each image, classifying each captured image cannotbe done by hand and computerized classifiers must be used.

The discussion above is merely provided for general backgroundinformation and is not intended to be used as an aid in determining thescope of the claimed subject matter. The claimed subject matter is notlimited to implementations that solve any or all disadvantages noted inthe background.

SUMMARY

A method includes receiving a satellite image of an area and classifyingeach pixel in the satellite image as representing water, land or unknownusing a model. For each of a plurality of possible water levels, a costassociated with the water level is determined, wherein determining thecost associated with a water level includes determining a number ofpixels for which the model classification must change to be consistentwith the water level and determining a difference between the waterlevel and a water level determined for the area at a previous timepoint. The lowest cost water level is selected and used to reclassify atleast one pixel.

In accordance with a further embodiment, a method includes classifyinglow-resolution pixels of a low-resolution satellite image of ageographic area to form an initial classification map and selecting atleast one physically-consistent classification map of the low-resolutionpixels based on the initial classification map. A water level associatedwith at least one of the physically-consistent classification maps isthen used to identify a set of high-resolution pixels representing aperimeter of water in the geographic area.

In accordance with a still further embodiment, a system includes aclassifier receiving a low-resolution image of a geographic area andclassifying each pixel of the image to form an initial classificationmap and a comparison module comparing the initial classification map toa plurality of physically-consistent classification maps to select aphysically-consistent classification map. A high-resolution classifierclassifies high-resolution pixels of the geographic area based on theselected physically-consistent classifier map.

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a bathymetric map of Medicine Lake in California.

FIG. 2 is an illustrative example showing different physicallyconsistent set of labels for a given elevation ordering.

FIG. 3 is an illustrative example showing a physically-consistent labelcorrection process.

FIG. 4 is an illustrative example showing limitations ofphysically-consistent label correction when temporal context is notapplied.

FIG. 5 is an illustrative example showing the utility of incorporatingtemporal context in an elevation-based label correction process.

FIG. 6(a) is a graph of true water levels in an area as a function oftime.

FIG. 6(b) is a graph of initial water level classifications over time.

FIG. 6(c) shows graphs of total cost, mismatch cost, and transitioncosts as a function of a.

FIGS. 6(d)-6(h) show graphs of corrected classifications over time usingdifferent values of α.

FIG. 7 is relative elevation ordering for KajaKai Reservoir, Afghanistanfrom SRTM's Digital Elevation data at 30 m spatial resolution with anoverlay of corresponding MODIS pixels at 500 m spatial resolution.

FIG. 8(a) shows a MODIS scale surface extent map of KajaKai Reservoir,Afghanistan overlaid on a Landsat (30 m resolution) composite image.

FIG. 8(b) shows a high-resolution water extent map obtained from ourmethod.

FIG. 9 is a diagram of a satellite image classification system used inthe various embodiments.

FIG. 10 provides a flow diagram for generating high-resolutionclassification maps from low-resolution images.

FIG. 11 provides a flow diagram for generating dictionaries ofphysically-consistent low-resolution classification maps with associatedwater levels.

FIG. 12 is a block diagram of a computing device used in the variousembodiments.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Accuracy of pixel classifications is limited due to various factors suchas noise and outliers, large amounts of missing data (due to clouds andsensor failures), lack of representative training data, and appropriateclassification models that can handle the high spatial and temporalheterogeneity at a global scale. Moreover, due to resource constraintsand physical limitations in sensor design, a single dataset does notprovide desired spatial and temporal resolution to create surface extentproducts required by various applications. For example, the ETM+ sensoron-board the LANDSAT 7 satellite captures earth observation data at 30 mspatial resolution every 16 days. On the other hand, the MODIS sensoron-board Terra and Aqua satellites captures data at much coarser spatialdetail (500 m) but every day. The multi-source nature of this data poseschallenges in extracting information at the desired level of spatialdetail and temporal frequency. Some prior methods rely on learning amapping between low-resolution data and high-resolution data attime-steps when both datasets are available and use this mapping intime-steps when only low-resolution data is available. This constraintof overlapping time-steps has two key limitations. First, in most realsituations, a single snapshot in time can have a large amount of noiseand missing data and hence might not have enough information to learnrobust mapping between two resolutions. Second, it limits theinformation transfer process to only the duration where both datasetsare available.

In the various embodiments, we present a new methodology that usesrobust physical principles governing surface water dynamics to overcomethe challenges in transferring information across complementarydatasets. Specifically, the embodiments provide two new methods thatexploit relative ordering among instances (due to elevation structure)to effectively transfer information between multiple sources.

In the various embodiments, the elevation structure (bathymetry) of awater body is used to provide a very robust physical constraint thatimproves the accuracy of the classification maps. Elevation of ageographical location on earth is its height above a certain fixed point(e.g. elevation above sea level). Earth's surface is highly uneven andhas various bowl shaped depressions called basins. Water bodies areformed when water fills these basins. Hence, locations inside and aroundthe water have varying elevation/depth. For example, FIG. 1 shows thisdepth information (called bathymetry) of Medicine Lake in Californiausing contour lines to represent locations that are at the sameelevation. This elevation information of locations introduces aninherent ordering in the locations. This ordering constraint determineshow a water body grows or shrinks. The key idea is the following:

if a location is filled with water then by laws of physics all thelocations in the basin that have lower elevation than the given locationshould also be filled with water. Thus, if we have elevation informationthen we can detect inconsistent class labels that do not adhere to thisphysical constraint.

Next we describe the mathematical formulation used to improve theaccuracy of labels using elevation ordering. Given elevation ordering(π) and the set of potentially erroneous labels at any given time stept, the aim is to estimate correct labels that are physically consistentwith the elevation ordering. For a given elevation ordering of Ninstances there are only N+1 possible sets of labels that are physicallyconsistent. For example, FIG. 2 shows eight possible sets ofphysically-consistent labels 202 for an elevation ordering 200 of sevenlocations. In each set of physically-consistent labels 202, land isrepresented by the number 0 and no hatching and water is represented bythe number 1 and hatching. Each physically-consistent set of labels canbe equally represented by the number of water pixels (θ) in the set. Forexample if we know the number of water pixels in the set to be k, thenby definition it will be the deepest k locations. In the absence of anyexternal information about the correct labels, the methodology makes anassumption that majority of the labels are correct and hence selects theset of physically consistent labels that matches the most with inputerroneous labels. For example, FIG. 3 shows an erroneous set of inputlabels 300 and a collection 302 of eight possible sets ofphysically-consistent labels. Of the eight possible sets ofphysically-consistent labels, set 304 has the largest number ofclassifications that match the input labels. As such, a method thatselects the physically-consistent labels based only on the closest matchwill select set 304 as the output set 306. Hence, in this illustrativeexample, location F is detected as erroneous and its label is changedfrom water to land.

Next, we describe two embodiments that make use of this elevation-basedordering to further improve the quality of the surface extent maps,which are also referred to as classification maps.

A. Information Transfer Across Time

The elevation based label correction methodology as described above usesestimated relative ordering to correct inconsistencies in each time stepindependently. Since, MODIS-based classification maps at daily scale canhave lots of errors and missing data due to clouds and other atmosphericdisturbances, correcting each time step independently is quitechallenging and can lead to abrupt changes in surface extents. Considerthe illustrative example shown in FIG. 4 where table 400 shows the truelabels for locations A-G, table 402 shows the initial classificationsgiven to the locations including “missing” classifications indicated bycross hatching for locations obscured by clouds, and table 404 shows thecorrected classifications by identifying the physically-consistentclassification that requires the fewest changes to the initialclassification. As shown, an algorithm based only on minimizing changesfrom the initial classification to the physically-consistentclassification can identify the wrong water level.

In most situations, a water body grows and shrinks smoothly (exceptsudden events such as floods) i.e. a lake area is likely to have a verysimilar extent over the course of two weeks. Hence, we need methods thatincorporate the dual objective of correcting mistakes while ensuringtemporal consistency in surface extent variations over time.

FIG. 5 shows the impact of incorporating temporal information in thecorrection process. In table 500 of FIG. 5, the true labels of locationsA-G are provided and in table 502 an initial classification of thelocations is provided. In table 504, the results of correcting theinitial classification while applying a physically-consistent constraintwithout applying a temporal constraint is shown, which arrives at thewrong water level. In table 506, the results of correcting the initialclassification while applying both a physically-consistent constraintand a temporal constraint is shown, which arrives at the correct waterlevel.

In general, if a water body has N locations then there are N+1 possiblewater levels for each time step. Further, if the water body has beenobserved for T time steps, then there are exponential (N^(T)) possibleconfigurations of water levels for the given water body over time. Ourgoal is to find that configuration of water levels over time that notonly show good consistency with input labels (water levels that lead tolower corrections in input labels) but also show good temporalconsistency (smoothly changing water levels). Both of these goalsconflict with each other. The configuration over time that leads to thebest consistency with input labels is obtained when each time step iscorrected independently (as explained in the previous section) but wouldlead to the less temporally consistent water levels. On the other hand,the most temporally-consistent configuration is obtained when all thelevels are forced to be constant (no dynamics in surface extents) butwould lead to worse consistency with input labels.

Mathematically, given an elevation ordering (π) and water levels for Ttime steps (θ_(1 . . . T)), the consistency with the input labels can berepresented as

$\begin{matrix}{{{Cost}_{mismatch}(T)} = {\sum\limits_{t = 0}^{T}\; {{Err}\left( {\theta_{t}\hat{\pi}} \right)}}} & (1)\end{matrix}$

where Err(θ, {circumflex over (π)}) represents number of inconsistenciesdetected by choosing water level θ_(t) for time step t.

The criteria to measure temporal consistency can be formulated as

$\begin{matrix}{{{Cost}_{transition}(T)} = {\sum\limits_{t = 0}^{T - 1}\; \left| \left( {{\hat{\theta}}_{t} - {\hat{\theta}}_{t + 1}} \right) \right|}} & (2)\end{matrix}$

The above criterion favors water levels in nearby time steps to besimilar and hence enforces temporal consistency.

Overall, we intend to find the configuration of water levels thatminimizes both objective functions

$\begin{matrix}{{\underset{{\hat{\theta}}_{1\ldots \; T}}{argmin}\mspace{14mu} {{Cost}_{mismatch}(T)}} + {\alpha \; {{Cost}_{transition}(T)}}} & (3)\end{matrix}$

where α is a trade-off parameter or weight between the two costs. So,when α is increased, the criterion will favor water levels that are moretemporally consistent and when α is decreased, the criterion will favorwater levels that better match the initial classification. Hence, as ais increased, Cost_(transition) decreases and Cost_(mismatch) increases.The above objective can be optimally solved for any given value of αrecursively using dynamic programming. Specifically, the water level atthe last time step T is defined as

$\begin{matrix}{{\hat{\theta}}_{T} = {\underset{k \in {\lbrack{0,N}\rbrack}}{argmin}\mspace{14mu} {{Cost}\left( {{\hat{\theta}}_{T} = k} \right)}}} & (4)\end{matrix}$

where, Cost({circumflex over (θ)}_(T)=k) can be recursively defined as

$\begin{matrix}{{{Cost}\left( {{\hat{\theta}}_{T} = k} \right)} = \left. {{\underset{l \in {\lbrack{0,N}\rbrack}}{argmin}\mspace{14mu} {{Cost}\left( {{\hat{\theta}}_{t - 1} = l} \right)}} + \alpha} \middle| {k - l} \middle| {+ {{Err}\left( {{\theta_{T} = k},\hat{\pi}} \right)}} \right.} & (5)\end{matrix}$

Given the optimum value of {circumflex over (θ)}_(T) is known, it can beused to determine the optimum value of using the following equation

$\begin{matrix}{{\hat{\theta}}_{T - 1} = \left. {{\arg \mspace{14mu} {\min\limits_{l \in {\lbrack{0,N}\rbrack}}\mspace{14mu} {{Cost}\left( {{\hat{\theta}}_{T - 1} = l} \right)}}} + \alpha} \middle| {k - l} \middle| {+ {{Err}\left( {{\theta_{T} = k},\hat{\pi}} \right)}} \right.} & (6)\end{matrix}$

FIG. 6 shows the performance of this algorithm on a synthetic datasetfor different values of α. FIG. 6(a) provides a ground truth of waterlevels (light colored) with water levels shown on the vertical axis andtime shown along the horizontal axis. FIG. 6(b) shows an initial noisyclassification of the locations shown in FIG. 6(a), showing a number oferrors at each time point. FIG. 6(d) shows a corrected classificationmap with α=0, indicating that only the Cost_(mismatch) is used. FIGS.6(e), 6(f), 6(g), and 6(h), show corrected classification maps forprogressively larger values of a showing that the accuracy of theclassification maps increases with increases in a up to the largestvalue of α=0.4 shown in the figures. FIG. 6(c) shows changes in thetotal cost 600, the Cost_(mismatch) 602 and the Cost_(transition) 604 asa function of α, which is shown on the horizontal axis. CAs we can see,as the value of a is increased, the Cost_(transition) goes down whereasCost_(mismatch) increases. Furthermore, initially, Cost_(transition)decreases at a very fast rate whereas Cost_(mismatch) increases at avery slow rate which implies that much more temporally consistent waterlevels can be obtained by very little increase in Cost_(mismatch). Ingeneral, these error curves can be used to determine the suitable valueof α. Specifically, the value of a should be increased only till thereis sufficient reduction in transition cost while not increasing flipcost significantly. As we can see, this method improves the accuracy ofthe maps than those produced by our previous approach as the error rategoes down from (0.18 for α=0 to 0.04 for α=0.4).

Thus, rich temporal context provided by the daily temporal resolution ofMODIS data can be effectively used to improve the accuracy of the labelsat low-resolution.

B. Information Transfer Across Space

The surface extent maps produced using the method above would giveaccurate maps but at low spatial detail (500 m). The elevation orderingconstraint can be used to even improve the resolution of these extentmaps. Specifically, if the elevation constraint is available athigh-resolution, then it can be used to convert binary labels atlow-resolution to binary labels at high-resolution. Assuming theelevation ordering does not change over time, this method does notrequire the high-resolution information and low-resolution informationto be present concurrently and hence can be used in more generalscenarios.

FIG. 7 shows elevation structure of KajaKai Reservoir in Afghanistan at30 m resolution with the low-resolution MODIS grid (500 m) overlaid ontop of it. Each grid cell is a low-resolution pixel in the MODISsatellite images and each low-resolution pixel roughly contains 256high-resolution pixels in the 30 m resolution images.

Initially, we assume that with perfect data and no errors inclassification, a cell/pixel at low-resolution will be labelled as waterif it has more than a certain number of high-resolution cells/pixels(threshold wth) within it that contain an image of water. In the mostgeneral settings, each low-resolution cell can have different thresholdsthat can also vary with time due to varying spectral properties of theland cover types enclosed within low-resolution cell. Here, we make anassumption that on any given time steps all locations have the samethreshold but this threshold can vary over time.

Method 1

Next, we describe a first methodology that uses elevation ordering totransfer information across space. The method has two main steps

1) Step 1. Prepare Dictionary of all possible physically consistentlow-resolution extents: Given the high-resolution ordering, ahigh-resolution classification map can be constructed for each possiblewater level, where each pixel is classified as either water or landbased on the selected water level. In one embodiment, f there are Nlocations at high-resolution, then there will be N+1 possible waterlevels (equivalently N+1 high-resolution classification maps). Now, fora single value of pixel count threshold wth, each high-resolutionclassification map can be converted into its correspondinglow-resolution classification map by grouping high-resolution pixelsinto the corresponding low-resolution pixel, counting the number ofhigh-resolution pixels that contain water, and comparing that number tothe pixel count threshold. When the number of high-resolution pixelsthat contain water exceeds the threshold, the correspondinglow-resolution pixel is classified as water. Otherwise, thecorresponding low-resolution pixel is classified as land. Note that twodifferent high-resolution classification maps associated with differentwater levels but the same pixel count threshold can lead to the samelow-resolution classification map. This information is stored in adirectory where each low-resolution classification map is linked to thewater levels that can generate it. This process is repeated for allvalues of the pixel count threshold wth and a dictionary correspondingto each value of the pixel count threshold is prepared.2) Step 2. Compare erroneous input low-resolution map with all possiblephysically consistent maps: Step 1 provides the list of all possiblephysically-consistent low-resolution classification maps together withwater levels that can generate them. In this step, we compare an initiallow-resolution classification map that may include one or more physicalinconsistencies with all of the physically-consistent low-resolutionclassification maps across all dictionaries. There can be multiplephysically-consistent low-resolution classification maps that can be abest match with the initial low-resolution classification map. To handlethis situation, we take the union of all water levels corresponding tothese best matches. Finally, using this selected set of water levels wecan estimate the high-resolution extents of the bodies of water in theinitial low-resolution classification map. The multiple values of waterlevels in the set implies that there is uncertainty in estimating thecorrect water level as all the water levels in the set would generateequally consistent low-resolution maps. Hence, we define an uncertaintybound. Specifically, we label all high-resolution locations below thelowest water level in the set (lower bound on water level) as water.Similarly, we label all locations above the highest water level in theset (upper bound on water level) as land. Locations that fall betweenthese bounds are labelled as unknown. The set of high-resolution pixelsclassified as water that border pixels labeled as unknown or land,define a perimeter of water in the high-resolution classification map.The set of high-resolution pixels classified as land that border pixelslabeled as unknown or water, define a perimeter of land in thehigh-resolution classification map.

FIG. 8 shows an illustrative example of the information transfer acrossspace process for KajaKai Reservoir on Jul. 5, 2015. In FIG. 8(a), aperimeter 800 of the Reservoir 802 is shown where perimeter 800 wasidentified using an initial low-resolution classification map. Inparticular, perimeter 800 is formed of low-resolution pixels classifiedas water that neighbor a low-resolution pixel classified as land. FIG.8(b) shows a high-resolution perimeter 804 for Reservoir 802, where thehigh-resolution perimeter is identified by selecting the lowest waterlevel associated with any of the physically-consistent low-resolutionclassification maps that best match the initial low-resolutionclassification map. This lowest water level is then used with thehigh-resolution elevation ordering of the Reservoir to identify whichhigh-resolution pixels would contain water at that water level. Theoutermost high-resolution pixels classified as water then form thehigh-resolution perimeter. Note that high-resolution perimeter 804 isdifferent from low-resolution perimeter 802. In particular, perimeter804 passes through the center of one or more of the low-resolutionpixels in low-resolution perimeter 802.

Ideally, we wish to have the smallest uncertainty gap possible (fewestnumber of pixels labeled as unknown). The size of the gap depends onvarious factors such as aggregation threshold (wth), shape and size ofthe lake, difference between resolutions. In the next section, weprovide some bounds on this uncertainty gap under some assumptions whichwill help in giving insights into the different aspects of thealgorithm.

Method 2

The second method for information transfer across space has five mainsteps: 1) Estimate elevation ordering at high spatial resolution (HSR).2) Estimate elevation ordering at low spatial resolution (LSR). 3)Estimate accurate and physically-consistent classification maps at LSR.4) Use elevation ordering at HSR from Step 1 and good qualityclassification maps at LSR from Step 3 to estimate confident labels atHSR and finally 5) Estimate remaining labels at HSR using elevationconstraint. Next, we describe these steps in detail.

Step 1. Estimate Elevation ordering at high spatial resolution({circumflex over (π)}_(h))

In this step, noisy binary classification maps at HSR and low temporalresolution (H_(i)) are used to learn high resolution elevation orderingusing an expectation-maximization framework. Note that if a high qualityelevation structure is available from any external source it can be usedinstead of estimating the high resolution elevation structure based onthe noisy classification maps.

Step 2. Estimate Elevation ordering at low spatial resolution({circumflex over (π)}_(l))

One way to estimate {circumflex over (π)}_(l) would be to use anExpectation-Maximization framework with noisy binary classification mapsat LSR and high temporal resolution (Li) similar to Step 1. However, weestimate {circumflex over (π)}_(l) using {circumflex over (π)}_(h) andL_(i) as it allows us to 1) estimate the threshold wth together with{circumflex over (π)}_(l) and 2) ensure that ordering learned at LSR iscoherent with ordering at HSR.

Each LSR pixel contains a number of HSR pixels (gr) where each of the grpixels have a ranking from {circumflex over (π)}_(h). Using {circumflexover (π)}_(h), LSR pixels can be ranked in a number of ways. Forexample, LSR pixels can be ranked based on the lowest rank HSR pixelwithin each LSR pixel. Similarly, they can be ranked using the highestrank HSR pixel within each LSR pixel. Here, we proposed to generatepossible LSR orderings on the basis of assumption A1. Specifically, wedefine a LSR ordering π_(l) ^(wth) as the ordering obtained by using HSRpixels with local rank wth within each LSR pixel. Thus, there can be grpossible LSR orderings that can be generated from {circumflex over(π)}_(h).

In the absence of any external information about the correct labels, weselect that LSR ordering that leads to the least amount of correctionsin L₁. This would also automatically provide the estimate of wth thatwill be used in next steps of the algorithm. Specifically, wth valuecorresponding to the selected LSR ordering is chosen as the cut-offthreshold.

Step 3: Estimate accurate and physically consistent classification mapsat LSR (L_(o))

Once the LSR ordering is estimated in the previous step, we can use itto correct each classification map (L_(i)) individually to obtainphysically consistent classification maps at LSR (L_(o)). Thesecorrections can be made using only the mismatch cost between thephysically consistent classification maps and the noisy classificationmaps or by using a combination of the mismatch cost and the transitioncost as discussed above. This step improves the quality of the resultingHSR maps because if the information in the LSR maps is of bad qualitythen it will get propagated in the estimated HSR maps as well.

Step 4. Estimate confident labels in HSR and high temporal resolution(Ĥ_(o))

Assuming a LSR pixel can be labelled as water only if it has at leastwth HSR water pixels, if we are given a LSR pixel labelled as water,then at least wth HSR pixels within it should be water. By definition,these wth instances will be filled according to their elevation rank(deeper to shallower/lower to higher). Similarly, if a LSR pixel islabelled as land then at least gr-wth HSR pixels within it should beland. Using this knowledge, we can confidently estimate physicallyconsistent labels for some of the HSR pixels within each LSR pixel.

Step 5. Estimate remaining labels in Ĥ_(o)

After Step 4, there will be a lot of unknown labels in Ĥ_(o). Forexample, if wth is gr/2, then half of the labels in Ĥ_(o) would beunknown after Step 4. In this final step, we use {circumflex over(π)}_(h) to estimate the labels of remaining instances. Specifically, wefirst find the shallowest (highest) HSR pixel that is labelled as water(Pivot_(w)) and label all the instances deeper (lower) than it as wateras well due to the physical constraint. Using the same rationale, wefind the deepest (lowest) HSR pixel labelled as land (Pivot_(l)) andlabel all instances shallower than it as land as well. This stepsignificantly reduces the number of unknown labels.

Finally, instances that are between pivots Pivot_(w) and Pivot_(l)remain unlabeled. Note that the elevation of Pivot_(l) will always behigher that the elevation of Pivot_(w) because Step 4 ensures that onlyphysically consistent labels are estimated. Ideally, the gap betweenPivot_(l) and Pivot_(w) should be as small as possible.

Analysis of Information Transfer Across Space A. Claim

Given an elevation ordering at high-resolution (which is independent ofthe mapping grid) and perfect binary labels at low-resolution (createdusing a given threshold, wth), the estimated high extent map using ourmethod will have unknowns only at the perimeter of the true extent withthe probability

$1 - \left\lbrack \left. \left( \frac{M - 1}{M + 1} \right) \middle| P_{L}^{i} \middle| {+ \left( \frac{M}{M + 1} \right)} \middle| P_{L}^{i} \middle| {- \left( \frac{M - 2}{M + 1} \right)} \middle| P_{L}^{i} \right| \right\rbrack$

B. Definitions

Perimeter: Perimeter of a given surface extent map is defined as theunion of the pixels in the neighborhood of the water pixels at theboundary of the extent. P_(L) ^(i) represents set of pixels atlow-resolution that are the perimeter of the low-resolution extent i.Similarly, P_(H) ^(i) represents set of pixels at high-resolution thatare the perimeter of the high-resolution extent i.

M: M is the number of high-resolution pixels in a low-resolution pixel.

Transition Pixel: A high-resolution pixel within each low-resolutionpixel corresponding to level wth.

Global Water Pivot: deepest water level in the selected set of waterlevel in the Step 2 of the algorithm.

Global Land Pivot: shallowest water level in the selected set of waterlevel in the Step 2 of the algorithm.

So, given these definitions, the claims suggests that the extents withlarger perimeter at low-resolution will have high probability ofrestricting the errors on the perimeter. Similarly, as the ratio of thetwo grids gets smaller (M gets smaller), the probability will increase.C. Proof

Key Observations

1) If a pixel's label is known to be water then all the pixels deeperthan the given pixel should also be water due to the physical constraintof elevation ordering. Similarly, if a pixel's label is known to be landthen all the pixels shallower than the given pixel should also be land.2) Elevation structure follows the proximity assumption i.e. for a givenperimeter P_(H) ^(i), all the pixels enclosed by it are strictly deeperthan pixels in the perimeter. Similarly, pixels that are not enclosed bythe perimeter will be strictly shallower than pixels in the perimeter.In other words, a water body grows in layers (contours)3) Furthermore, due to this assumption, a pixel at high-resolution willalways have at least one neighbor that is shallower and at least oneneighbor that is deeper than the given pixel.4) By definition, for a given true high-resolution extent E_(H) ^(i),the shallowest high-resolution water pixel within a low-resolution pixelwill always be on the boundary of the E_(H) ^(i) (i.e. in the perimeterset P_(H) ^(i))5) The shallowest water pixel within a low-resolution pixel get assigneda label by Step 2 of the algorithm only if that pixel is the transitionpixel of that low-resolution pixel. If the shallowest pixel is deeperthan the transition pixel, then it implies that the water level is lessthan wth and hence no pixel will be labelled as water. On the otherhand, if the shallowest water pixel is shallower than the transitionpixel then only the transition pixel and pixels below it are labelled aswater.

So, given these observations, if Step 2 of the algorithm (assigninglabels to confident pixels using the aggregation threshold wth) is ableto assign water label to any of the pixels in P_(H) ^(i) (i.e. the pivotwater pixel is in the perimeter set, P_(H) ^(i)), then due toobservation 2, this would mean that all the pixels enclosed by theperimeter will be labelled as water. Similarly, if Step 2 of thealgorithm is able to assign land label to any of the pixels in theperimeter, then all the pixels that are outside of the perimeter willget labelled as land. Hence, in worst case, the unknown labels will beonly at the perimeter.

In general, if the above conditions hold, the number of unknowns caneven be less than the number of perimeter pixels. If there are somepixels in the perimeter set that are deeper than the pivot water pixelin the perimeter set, then they will get assigned a label as well.Similarly, for land. Thus, the claim provides the lower bound on thenumber of the unknown labels under aforementioned conditions.

Now, we derive the probability that the pivot water pixel and pivot landpixel are within the perimeter set.

A perimeter pixel at high-resolution will be assigned a water label onlyif one of the following two conditions hold true

C1. There exists a modis pixel that is filled till level wth Due toobservation 4, water pixels at the boundary of the true extent arealways the shallowest pixels within each low-resolution pixel. Due toobservation 5, the shallowest water pixel within a low-resolution pixelis assigned a label only when Condition 1 holds. Since, for theshallowest one of the water pixel at the boundary of true water extentat high-resolution will always be the shallowest pixel within the modispixel, it will be assigned a label due to observation 4.C2. There exists a modis pixel that is filled till level wth+1

In this case, the water pixel at the boundary of the true extent athigh-resolution will not be assigned water label due to observation 5,but due to observation 3, there will always be a pixel in itsneighborhood that will be equal to the transition pixel or a deeper thanthe transition pixel and hence will get labelled as water.

A perimeter pixel will be assigned a land label in the followingcondition

C3. There exists a low-resolution pixel that is filled till level wth−1

In this case, due to observation 5, the shallowest water pixel will notbe labelled, but pixels shallower than it in its neighborhood will belabelled as land due to observation 3.

To summarize, there should be at least one low-resolution pixel thatshould satisfy either Condition 1 or Condition 2 and there should be atleast one low-resolution pixel that satisfy Condition 3. In terms ofprobability

1−[P(!C1&!C2)+P(!C3)−P(!C1&!C2&!C3)]   (7)

Since, we make an assumption that the elevation structure is independentof the mapping grid, any given true extent at high-resolution E_(H) ^(i)can induce all possible water levels in the boundary pixels atlow-resolution (P_(L) ^(i)). In other words, the above assumptionimplies that the probability of a low-resolution pixel to be any waterlevel is 1/(M+1). Now, for a low-resolution pixel not be able to assignwater label to water pixel in the perimeter set P_(H) ^(i), it should bewater levels other than wth and wth+1 which has the probability(M+1−2/M+1). Now, For all low-resolution pixels in the low-resolutionparameter set (P_(L) ^(i)) to not be in levels wth or wth+1 is

$\begin{matrix}{{P\left( {{{{!{C\; 1}}\&}!}C\; 2} \right)} = \left. \left( \frac{M - 1}{M + 1} \right) \middle| P_{L}^{i} \right|} & (8)\end{matrix}$

Similarly, for all low-resolution pixels in P_(L) ^(i) to not be atlevel wth−1, the probability is

$\begin{matrix}{{P\left( {!{C\; 3}} \right)} = \left. \left( \frac{M}{M + 1} \right) \middle| P_{L}^{i} \right|} & (9)\end{matrix}$

Using the above equations, the probability that both global water pivotand global land pivot will be in the perimeter set P_(H) ^(i) is

$\begin{matrix}{1 - \left\lbrack \left. \left( \frac{M - 1}{M + 1} \right) \middle| P_{L}^{i} \middle| {+ \left( \frac{M}{M + 1} \right)} \middle| P_{L}^{i} \middle| {- \left( \frac{M - 2}{M + 1} \right)} \middle| P_{L}^{i} \right| \right\rbrack} & (10)\end{matrix}$

As we can see, the probability depends on number of pixels perimeter setat low-resolution. For example,

for M=100, |P_(L) ^(i)|=350, the probability is 0.96for M=225, |P_(L) ^(i)|=700, the probability is 0.95for M=400, |P_(L) ^(i)|=1500, the probability is 0.97

FIG. 9 provides a system diagram of a system used to improve theefficiency and accuracy of computer-based labeling technology thatautomatically labels satellite data to determine the extent of bodies ofwater. In FIG. 9, a satellite 900, positioned in orbit above the earthand having one or more sensors, senses values for a geographic location902 that is comprised of a plurality of geographic areas/smallergeographic locations 904, 906 and 908. Multiple sensors may be presentin satellite 900 such that multiple sensor values are generated for eachgeographic area of geographic location 902. In addition, satellite 900collects frames of sensor values for geographic location 902 with eachframe being associated with a different point in time. Thus, at eachpoint in time, one or more sensor values are determined for eachgeographic area/smaller geographic location in geographic location 902creating a time series of sensor values for each geographic area/smallergeographic location. Each frame of sensor values is alternativelyreferred to as an image of geographic location 902 with each sensorvalue representing a pixel in that image. This is true even when thesensor values represent visually imperceptible phenomena such asinfrared or ultraviolet electro-magnetic radiation.

A second satellite 950 positioned in orbit above the earth and havingone or more sensors, senses values for geographic location 902 at alower resolution than satellite 900 such that two or more of thegeographic areas in geographic location 902 are represented by a singlesensor value. Satellite 950 collects frames of sensor values forgeographic location 902 with each frame being associated with adifferent point in time. Each frame is alternatively referred to as animage of geographic location 902 with each sensor value representing apixel in that image. This is true even when the sensor values representvisually imperceptible phenomena such as infrared or ultravioletelectro-magnetic radiation. Note that because the images produced bysecond satellite 950 are a lower resolution, each pixel in the imagescreated by second satellite 950 represents a larger surface on earththan the pixels in the images generated by satellite 900.

Satellites 900 and 950 transmit the sensor values to a receiving dish910 or respective receiving dishes, which provide the sensor values to acommunication server 912. Communication server 912 stores the sensorvalues as frames of sensor values (images) 914 in a memory incommunication server 912. A labeling server 916 receives frames ofsensor values 914 and provides the received frames of sensor values to aclassifier 918, which uses a model 920 to classify each sensorvalue/pixel in each frame into one of a set of classes such as Land,Water or Unknown, thereby forming an initial classification map 922.

In accordance with one embodiment, initial classification map 922 isimproved by applying initial classification map 922 to a temporal andmismatch comparison module 924, which determines a temporal cost and amismatch cost for each of a set of physically-consistent classifier maps926 for each frame. The temporal cost for a frame is computed based onthe difference between the water level associated with thephysically-consistent classification map and a water level of aphysically-consistent classification map that was selected for atemporally neighboring frame. The mismatch cost is computed based on thedifferences between initial classification map 922 and thephysically-consistent classifier map. In one particular embodiment, themismatch cost is based on the number of pixels in initial classificationmap 922 that must have their initial classification changed if theclassification map is to be consistent with the water level associatedwith the physically-consistent classifier map. In accordance with oneembodiment, a recursion is performed across a series of frames toidentify the sequence of physically-consistent classification maps andassociated water levels 928 that provide the lowest combined temporalcost and mismatch cost as discussed above.

In accordance with a further embodiment, each initial classification map922 that is low-resolution is used to identify a high-resolutionclassification map 934. In particular, a comparison module 930,identifies one or more physically-consistent low-resolutionclassification maps 926 that are the lowest-cost physically-consistentclassification maps given the initial classification map 922. Inaccordance with one embodiment, the lowest-cost physically-consistentclassification maps are those maps that can be produced from initialclassification map 922 with the fewest changes to initial classificationmap 922. In other words, the lowest-cost physically-consistent maps arethose maps with the most classifications in common with and fewestdifferences with initial classification map 922.

In accordance with one embodiment, physically-consistent low-resolutionclassification maps 926 are constructed by a map constructor 938applying different water levels to a high-resolution depth/elevation map936 of the geographic area and setting classifications for thelow-resolution pixels based on which of the high-resolution pixels wouldcontain water at that water level. Specifically, for each water level,map constructor 938 identifies and counts the high-resolution pixels ineach low-resolution pixel that would contain water at that water level.The number of high-resolution pixels that would contain water is thencompared to a threshold count to determine if the low-resolution pixelshould be classified as water or land for the water level. Inparticular, if more than the threshold count of high-resolution pixelswould contain water, the low-resolution pixel is classified as water andif not, the low-resolution pixel is classified as land.

Note that a single physically-consistent low-resolution map can beassociated with multiple different water levels for the same thresholdcount. In other words, even though different numbers of high-resolutionpixels contain water at different water levels, the same low-resolutionclassification map is constructed. In accordance with one embodiment,map constructor 938 stores an association between eachphysically-consistent low-resolution map and all of the water levelsthat can produce the physically-consistent low-resolution map for aparticular threshold count. In some embodiments, a separate dictionaryof physically-consistent low-resolution maps is produced for eachthreshold count, where each dictionary provides a separate associationbetween physically-consistent low-resolution classification maps andwater levels.

When performing the comparison between initial classification map 922and physically-consistent low-resolution classification maps 926, it ispossible for comparison module 930 to identify multiplephysically-consistent low-resolution maps that are equally close toinitial classification map. This possibility, combined with thepossibility of any one physically-consistent low-resolutionclassification map being associated with multiple water levels, meansthat there is a set of equally-probable water levels that could haveproduced the frame of sensor values captured by the low-resolutionsatellite. To address this, a high-resolution classifier 932 forms aunion of all water-levels associated with all physically-consistentlow-resolution classification maps considered to be closest to initialclassification map 922 by comparison module 930. High-resolutionclassifier 932 then selects the lowest water level and the highest waterlevel in that union and applies the lowest water level to thehigh-resolution elevation/depth map 936 to identify high-resolutionpixels that would be covered by water at the lowest water level. Theoutermost high-resolution pixels covered by water (the high-resolutionpixels covered by water that neighbor high-resolution pixels that wouldnot be covered by water) are then designated as the perimeter of thewater. In some embodiments, high-resolution classifier 932 also appliesthe highest water level to the high-resolution elevation/depth map 936to identify high-resolution pixels that neighbor and are above pixelsthat would be covered with water at the highest water level. Thesepixels are then designated as a perimeter for land in thehigh-resolution classification map 934.

FIG. 10 provides a flow diagram for generating high-resolutionclassification maps 934 in accordance with one embodiment. In step 1000,dictionaries of low-resolution extents, such as physically-consistentclassification maps 926 are generated. FIG. 11 provides a flow diagramof a method for generating such dictionaries.

At step 1100, the high-resolution elevation map 926 is constructed forthe geographic area. This high-resolution elevation map provides anelevation structure of the geographic area that indicates the relativeheight of each high-resolution pixel. In a worst case, eachhigh-resolution pixel is at a separate height. In most circumstances,collections of high-resolution pixels are at the same height. At step1102, low-resolution satellite pixels are overlaid on thehigh-resolution elevation map. In other words, each high-resolutionpixel is assigned to one of the low-resolution pixels for a frame ofsensor values 914.

At step 1104, a pixel count threshold is selected. In accordance withone embodiment, the pixel count threshold is selected from a set ofpossible pixel count thresholds spanning from one to the total number ofhigh-resolution pixels in a complete low-resolution satellite image.

At step 1106, a water level is selected from a set of possible waterlevels. In step 1108, all high-resolution pixels in the low-resolutionimage that are filled at that water level are identified. At step 1110,a low-resolution pixel is selected and at step 1112, the high-resolutionpixels assigned to that low-resolution pixel are examined to determinehow many of the high-resolution pixels are filled at that water level.That number is then compared to the pixel count threshold. If the numberof high-resolution pixels filled with water exceeds the pixel countthreshold, the low-resolution pixel is classified as water in step 1114.If the threshold is not exceeded at step 1112, the low-resolution pixelis classified as land at step 1116. If there are more low-resolutionpixels to process at step 1118, the process returns to step 1110 toselect a different low-resolution pixel. If there are no morelow-resolution pixels at step 1118, the process continues at step 1120where the low-resolution map is stored as a physically-consistentclassification map 926 together with the water level. In accordance withone embodiment, before storing the low-resolution map, existingphysically-consistent classification maps 926 are compared to thelow-resolution map. In an existing physically-consistent classificationmap 926 is the same as the current low-resolution map, the water levelfor the current low-resolution map is simply added to the list of waterlevels associated with the physically-consistent classification map 926.In accordance with one embodiment, the physically-consistentlow-resolution classification maps 926 are grouped together indictionaries with a separate dictionary for each selected pixel countthreshold.

At step 1122, the process determines if there are more water levels, ifthere are more water levels, the process returns to step 1106 to selecta new water level and steps 1108-1122 are repeated. When there are nomore water levels at step 1122, the process determines if there are morepixel count thresholds at step 1124. If there are more pixel countthresholds, the process returns to step 1104 and steps 1106-1124 arerepeated. When there are no more thresholds, the process for generatingthe dictionaries of physically-consistent low-resolution maps ends atstep 1126.

Returning to FIG. 10, after generating the dictionaries ofphysically-consistent low-resolution classification maps, the process ofFIG. 10 continues at step 1002 where it receives a low-resolution imageor frame of sensor values 914. At step 1004, classifier 918 classifieseach low-resolution pixel of the frame of sensor values to produce aninitial classification map 922. At step 1006, comparison module 930selects the lowest-cost physically-consistent low-resolutionclassification maps given the initial classification map 922. Inaccordance with one embodiment, the lowest-cost physically-consistentlow resolution classification maps are the maps that require the fewestchanges to initial classification map 922 in order to form thephysically-consistent low resolution classification map. High-resolutionclassifier 932 then forms a union of the water levels associated withthe lowest-cost low-resolution classification maps at step 1008. At step1010, high-resolution classifier 932 sets the lowest water level in theunion as the water and at step 1012 identifies high-resolution pixelsthat are filled at that water level. The outermost such pixels are setas the perimeter of the water where an outermost pixel is a pixel thatneighbors at least one pixel that is not covered by water at that waterlevel. At step 1014, high-resolution classifier 932 sets the elevationlevel above the highest water level in the union of water levels as aland level. At step 1016, the high-resolution classifier 932 identifiesall high-resolution pixels at the land level that surround theidentified perimeter of water as a perimeter of land.

An example of a computing device 10 that can be used as a server and/orclient device in the various embodiments is shown in the block diagramof FIG. 12. For example, computing device 10 may be used to perform anyof the steps described above. Computing device 10 of FIG. 12 includes aprocessing unit (processor) 12, a system memory 14 and a system bus 16that couples the system memory 14 to the processing unit 12. Systemmemory 14 includes read only memory (ROM) 18 and random access memory(RAM) 20. A basic input/output system 22 (BIOS), containing the basicroutines that help to transfer information between elements within thecomputing device 10, is stored in ROM 18.

Embodiments of the present invention can be applied in the context ofcomputer systems other than computing device 10. Other appropriatecomputer systems include handheld devices, multi-processor systems,various consumer electronic devices, mainframe computers, and the like.Those skilled in the art will also appreciate that embodiments can alsobe applied within computer systems wherein tasks are performed by remoteprocessing devices that are linked through a communications network(e.g., communication utilizing Internet or web-based software systems).For example, program modules may be located in either local or remotememory storage devices or simultaneously in both local and remote memorystorage devices. Similarly, any storage of data associated withembodiments of the present invention may be accomplished utilizingeither local or remote storage devices, or simultaneously utilizing bothlocal and remote storage devices.

Computing device 10 further includes a hard disc drive 24, a solid statememory 25, an external memory device 28, and an optical disc drive 30.External memory device 28 can include an external disc drive or solidstate memory that may be attached to computing device 10 through aninterface such as Universal Serial Bus interface 34, which is connectedto system bus 16. Optical disc drive 30 can illustratively be utilizedfor reading data from (or writing data to) optical media, such as aCD-ROM disc 32. Hard disc drive 24 and optical disc drive 30 areconnected to the system bus 16 by a hard disc drive interface 32 and anoptical disc drive interface 36, respectively. The drives, solid statememory and external memory devices and their associatedcomputer-readable media provide nonvolatile storage media for computingdevice 10 on which computer-executable instructions andcomputer-readable data structures may be stored. Other types of mediathat are readable by a computer may also be used in the exemplaryoperation environment.

A number of program modules may be stored in the drives, solid statememory 25 and RAM 20, including an operating system 38, one or moreapplication programs 40, other program modules 42 and program data 44.For example, application programs 40 can include instructions forperforming any of the steps described above. Program data can includeany data used in the steps described above.

Input devices including a keyboard 63 and a mouse 65 are connected tosystem bus 16 through an Input/Output interface 46 that is coupled tosystem bus 16. Monitor 48 is connected to the system bus 16 through avideo adapter 50 and provides graphical images to users. Otherperipheral output devices (e.g., speakers or printers) could also beincluded but have not been illustrated. In accordance with someembodiments, monitor 48 comprises a touch screen that both displaysinput and provides locations on the screen where the user is contactingthe screen.

Computing device 10 may operate in a network environment utilizingconnections to one or more remote computers, such as a remote computer52. The remote computer 52 may be a server, a router, a peer device, orother common network node. Remote computer 52 may include many or all ofthe features and elements described in relation to computing device 10,although only a memory storage device 54 has been illustrated in FIG.12. The network connections depicted in FIG. 12 include a local areanetwork (LAN) 56 and a wide area network (WAN) 58. Such networkenvironments are commonplace in the art.

Computing device 10 is connected to the LAN 56 through a networkinterface 60. Computing device 10 is also connected to WAN 58 andincludes a modem 62 for establishing communications over the WAN 58. Themodem 62, which may be internal or external, is connected to the systembus 16 via the I/O interface 46.

In a networked environment, program modules depicted relative tocomputing device 10, or portions thereof, may be stored in the remotememory storage device 54. For example, application programs may bestored utilizing memory storage device 54. In addition, data associatedwith an application program may illustratively be stored within memorystorage device 54. It will be appreciated that the network connectionsshown in FIG. 12 are exemplary and other means for establishing acommunications link between the computers, such as a wireless interfacecommunications link, may be used.

Although elements have been shown or described as separate embodimentsabove, portions of each embodiment may be combined with all or part ofother embodiments described above.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described above.

What is claimed is:
 1. A method comprising: receiving a satellite imageof an area; classifying each pixel in the satellite image using a model;for each of a plurality of possible water levels, determining a costassociated with the water level, wherein determining the cost associatedwith a water level comprises: determining a number of pixels for whichthe model classification must change to be consistent with the waterlevel; and determining a difference between the water level and a waterlevel determined for the area at a previous time point; selecting thelowest cost water level; and using the selected lowest cost water levelto reclassify at least one pixel.
 2. The method of claim 1 whereindetermining the cost associated with a water level further comprisesapplying a weight to the determined difference between the water leveland the water level determined for the area at a previous time.
 3. Themethod of claim 2 further comprising selecting the weight to provide alowest cost.
 4. The method of claim 1 further comprising: receiving aplurality of satellite images of the area; beginning with a lastsatellite image in the plurality of images, recursively determining awater level for each satellite image of the area.
 5. The method of claim4 wherein recursively determining a water level for a satellite imagecomprises: for each of a plurality of possible water levels, determininga cost associated with the water level, wherein determining the costassociated with a water level comprises: determining a number of pixelsfor which a model classification must change to be consistent with thewater level; determining a difference between the water level and awater level for the area at a previous time point; and determining acost for the water level for the area at the previous time point; andselecting the lowest cost water level.
 6. A method comprising:classifying low-resolution pixels of a low-resolution satellite image ofa geographic area to form an initial classification map; selecting atleast one physically-consistent classification map of the low-resolutionpixels based on the initial classification map; and using a water levelassociated with at least one of the physically-consistent classificationmaps to identify a set of high-resolution pixels representing aperimeter of water in the geographic area.
 7. The method of claim 6wherein each of the physically-consistent classification maps of thelow-resolution pixels provides a set of low-resolution pixelsrepresenting a perimeter of the water in the geographic area that isdifferent from the perimeter of the water represented by thehigh-resolution pixels.
 8. The method of claim 7 wherein the perimeterof the water represented by the high-resolution pixels passes within alow-resolution pixel.
 9. The method of claim 6 wherein using the waterlevel associated with at least one of the physically-consistentclassification maps comprises using a lowest water level associated withany of the selected physically-consistent classification maps.
 10. Themethod of claim 6 wherein each selected physically-consistentclassification map is associated with a respective threshold number ofhigh-resolution pixels such that a low-resolution pixel in thephysically-consistent classification map is designated as land unless awater level associated with physically-consistent classification mapwill cause more than the threshold number of high-resolution pixels inthe low-resolution pixel to contain water.
 11. The method of claim 10wherein the at least one selected physically-consistent classificationmaps comprise at least two physically-consistent classification mapswith different associated threshold numbers of high-resolution pixels.12. The method of claim 6 further comprising: using a second water levelassociated with at least one of the selected physically-consistentclassification maps to identify a set of high-resolution pixelsrepresenting a perimeter of land in the geographic area.
 13. The methodof claim 6 wherein selecting at least one physically-consistentclassification map of the low-resolution pixels based on the initialclassification map comprises selecting a physically-consistentclassification map based on a number of differences between thephysically-consistent classification map and the initial classificationmap.
 14. The method of claim 13 wherein a plurality ofphysically-consistent classification maps of the low-resolution pixelshave the same number of differences when compared to the initialclassification map.
 15. A system comprising: a classifier receiving alow-resolution image of a geographic area and classifying each pixel ofthe image to form an initial classification map; a comparison modulecomparing the initial classification map to a plurality ofphysically-consistent classification maps to select aphysically-consistent classification map; and a high-resolutionclassifier classifying high-resolution pixels of the geographic areabased on the selected physically-consistent classifier map.
 16. Thesystem of claim 15 wherein the high-resolution classifier classifies thehigh-resolution pixels by selecting a water level associated with thephysically-consistent classification map and determining whichhigh-resolution pixels would contain water at that water level.
 17. Thesystem of claim 15 wherein the comparison module selects a plurality ofphysically-consistent classification maps and the high-resolutionclassifier classifies the high-resolution pixels based on the pluralityof selected physically-consistent classifier maps.
 18. The system ofclaim 17 wherein at least one of the physically-consistent classifiermaps is associated with multiple water levels.
 19. The system of claim18 wherein the high-resolution classifier classifies the high-resolutionpixels by identifying a lowest water level associated with any of theselected physically-consistent classifier maps and determining whichhigh-resolution pixels would contain water at that lowest water level.20. The system of claim 19 wherein the high-resolution classifierclassifies the high-resolution pixels by identifying a highest waterlevel associated with any of the selected physically-consistentclassifier maps and determines which high-resolution pixels would notcontain water at that highest water level.